Question

The internal energy of a diatomic gas us given as $U=U_{0}V$, where $U_0$ is a constant . Molar heat capacity of gas is

• A. $\frac{5}{2}R$
• B. $\frac{7}{2}R$
• C. $\frac{9}{2}R$
• D. $\frac{3}{2}R$

Answer 1

The correct option is A $\frac{5}{2}R$

It is given that $U=U_{0}V$

For a diatomic molecule, internal energy is given by

$U=\frac{5}{2}nRT$

$U_{0}V=\frac{5}{2}nRT$

Taking derivative on both sides.

$U_0\frac{dV}{dT}=\frac{5}{2}Rn$

$C_v=\frac{5}{2}R(\because \frac{U_{0}dU}{ndT}=C_v)$

Hence, molar heat capacity is $\left[\frac{5}{2}R\right]$.